## 7.04.2011

### The Momentum Externality

I liked this new NBER working paper that was presented at the recent Stanford meeting.
Pounds that Kill: The External Costs of Vehicle Weight
Michael Anderson, Maximilian Auffhammer
NBER Working Paper No. 17170
Heavier vehicles are safer for their own occupants but more hazardous for the occupants of other vehicles. In this paper we estimate the increased probability of fatalities from being hit by a heavier vehicle in a collision. We show that, controlling for own-vehicle weight, being hit by a vehicle that is 1,000 pounds heavier results in a 47% increase in the baseline fatality probability. Estimation results further suggest that the fatality risk is even higher if the striking vehicle is a light truck (SUV, pickup truck, or minivan). We calculate that the value of the external risk generated by the gain in fleet weight since 1989 is approximately 27 cents per gallon of gasoline. We further calculate that the total fatality externality is roughly equivalent to a gas tax of \$1.08 per gallon. We consider two policy options for internalizing this external cost: a gas tax and an optimal weight varying mileage tax. Comparing these options, we find that the cost is similar for most vehicles.
And the important number from the intro (it was left out of the abstract):
When we translate this higher probability of a fatality into external costs (relative to a small baseline vehicle), the total external costs of vehicle weight from fatalities alone are estimated at \$93 billion per year
The focus of the paper's second half in on the design of policies that might correct this externality, which I really like because it makes the results instantly usable.

One thing that I think could enrich the paper further is if the authors discussed this result with a some attention to the physics of inelastic collisions.  One reason this might be useful is that it instantly points to a second policy option that is not addressed in the paper: changing speed limits.  In a collision, it's the momentum of the colliding cars that matters if we're thinking about the amount of kinetic energy that's available to kill the people in the cars.  As the paper rightly points out, momentum (and thus available kinetic energy) increases with vehicle mass.  But momentum is the product of mass and velocity.  So we could, in theory, maintain fatality rates while increasing average vehicle weight so long as we decreased speed limits.  The effect of vehicle speed on accident fatalities (via its influence on momentum) was shown in Ashenfelter and Greenstone's JPE paper.  I'm not sure if Americans would prefer to drive slower in bigger cars, but I think its worth pointing out that there is a tradeoff between mass and velocity (when one is talking about fatality risks).  These two papers are looking at two sides of the same coin: momentum.